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Hitman42 [59]
3 years ago
5

What is the scale factor of AABC to A DEF?

Mathematics
1 answer:
Tasya [4]3 years ago
5 0

Answer: D

Step-by-step explanation:

the scale factor is 6

Triangle ABC  has the lengths  4,2,4   and DEF has the lengths 24,12,24

so for the triangle ABC's lengths to become triangle DEF  is is supposed to be multiplied by 6

4*6= 24

2*6= 12

4*6= 24

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A truncated cone has horizontal bases with radii 18 and 2. A sphere is tangent to the top, bottom, and lateral surface of the tr
MariettaO [177]
<h3>Answer:  6 units</h3>

===================================================

Explanation:

A truncated cone is where we start with a regular 3D cone and chop off the top. The portion up top is a smaller cone, which we'll ignore. The bottom part is the truncated cone portion.

In the real world, a lampshade is one example of a truncated cone.

----------------

Let x be the radius of the sphere.

We'll be focusing on a vertical cross section of the truncated cone. Refer to figure 1 in the diagram below.

We have the following points

  • A = center of the sphere
  • B = center of the circular base of the truncated cone
  • C = point 18 units to the right of point B
  • E = point directly above point A, and its the center of the circular top of the truncated cone
  • D = point 2 units to the right of point E
  • F = the location where the circle touches the slanted curved side of the truncated cone
  • G = point directly below point D, and located on segment BC

We'll connect a few of those points forming the dashed lines in figure 1.

To start off, draw a segment from D to G. This forms rectangle BGDE with sides of EB = 2x and BG = 2. The side BC is 18 units, so that must mean GC = BC - BG = 18 - 2 = 16.

Since EB = 2x, this means DG is also 2x.

------------------

Now focus on triangles ABC and AFC. They are congruent right triangles. We can prove this using the HL (hypotenuse leg) theorem. Recall that the radius of a circle is perpendicular to the tangent line, which is why angle AFC is 90 degrees. Angle ABC is a similar story.

Because they are congruent right triangles, this indicates side BC is the same length as side FC. Therefore, FC = 18

Through similar logic, triangles ADE and ADF are congruent as well which leads to ED = FD = 2.

Combine sides FD and FC to get the length of DC

DC = FD+FC = 2+18 = 20

This is the hypotenuse of the right triangle GCD

------------------

After all that, we have the right triangle GCD with the legs of 2x and 16. The hypotenuse is 20. Refer to figure 2 shown below.

As you can probably guess, we'll use the pythagorean theorem to find the value of x.

a^2 + b^2 = c^2

(DG)^2 + (GC)^2 = (CD)^2

(2x)^2 + (16)^2 = (20)^2

4x^2 + 256 = 400

4x^2 = 400-256

4x^2 = 144

x^2 = 144/4

x^2 = 36

x = sqrt(36)

x = 6 is the radius of the sphere.

7 0
2 years ago
The formula to convert °F to °C is C = C equals StartFraction 5 Over 9 EndFraction left-parenthesis F minus 32 right-parenthesis
lora16 [44]
50 degrees celsius converted to fehranheit is 122 degrees
5 0
3 years ago
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Find the slope of a line passing though the given points (1,4) (3,2)
kifflom [539]
I believe the slope is -1
4 0
3 years ago
Find m∠U.<br> Write your answer as an integer or as a decimal rounded to the nearest tenth.
Ilia_Sergeevich [38]

Answer:

∠U = 56.4

Step-by-step explanation:

We can use trigonometric functions to solve this

Here we are given the opposite side of ∠U as well as the adjacent side.

When dealing with the adjacent and opposite side we use sin

Sin = Opposite side / Adjacent side

Opp = 5 and adj = 6

So

Sin(U) = 5/6

* take the inverse sine of both sides *

arc(sin)(u) = u

arcsin(5/6) = 56.4 *( rounded to the nearest tenth )

∠U = 56.4

5 0
2 years ago
Read 2 more answers
Please help ASAP give you 20 points and brainiest
GuDViN [60]

Answer:

Total charge= -25

Step-by-step explanation:

Given :

Charges of some ions

Aluminium    +3

Phosphate     -3

Chloride         -1

Silver               +1

To find total charge on 8 phosphate,7 chloride and 2 Aluminium atoms

Aluminium    +3 × 2 =+6

Phosphate     -3 × 8 = -24

Chloride         -1 × 7 = -7

total charge=

+6-24-7 =+6 -31

= -25

6 0
3 years ago
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